Exactly. The centre of that map would probably have a kids park with pathways connecting to all 4 segments.
Nice, but in my experience of the USA, which is of course hardly comprehensive, being constrained by class and my father's USAF career (so that the only big city I ever got a good look at was Los Angeles as a kid, Air Force bases tend to be in the boonies) we would not do that. All the parks and so forth I know are just on the street, it is almost unthinkable to have pedestrian paths cars can't drive down.
Might be different in places like New England--I've technically resided in New England, but it was on Loring AFB, way up in the far northeast corner of Maine; aside from the base itself the mighty metropolis of Caribou (hundreds of residents? Thousands?) was the closest thing nearby, with Bangor, better known to popular culture followers in its disguised form as Stephen King's fictitious Castle Rock, was the off-base bright lights and big city, a hundred miles away--an Air Force family magazine listing characteristics of the various bases in the late '70s simply listed Loring as "200 miles from Boston!") I was there between the ages of 3-5 and we just did not go off base that much, indeed the base itself was probably the greatest metropolis south of the Canadian border and north of Bangor.
Mostly I lived in various "suburbs" as a kid. In '74-75 when I was in fourth grade I lived in the vincinity of Whittier, CA, near the Los Angeles-Orange county border, and I used to bicycle to school and wander around various parts of town after school, the YMCA and Whitwood branch of the Whittier library system was, I don't know I'd have to use Google Earth or something, but a pretty long bike ride from my (Catholic) school.
Every damn thing in Whittier was grids, not always the same grids and not always continuous to be sure. But there were absolutely none of these nifty Wardrobe Route to Narnia ways of sneaking between cul de sacs.
The majority of my childhood years were in two neighborhoods near the vast urban giant of Panama City, Florida, home of...OK I can't mention
that. As it happened, when I lived there, both places were being pretty recently developed, and we did have a very large backyard with lots of big trees in it, and I could go over the fence to a rather cool little stretch of woods with some impromptu beaten trails on it, and pop up in the middle of a trailer part on one of the branches of US Hwy 98. In another direction was a road that went down what must be the only hill in coastal Florida, 50 feet down or so, to run along pretty empty woods with more trails, burned out cars, pits in the ground, till we got to another road with the elementary school on it. (Never went there, went to Catholic school beyond the great center of PC itself, the old St Andrews bay neighborhoods).
If I continued down that road, on my bike, past two very busy highways, I came to another neighborhood with swamp and medium sized alligators (no, I had no idea they could actually chase me and eat me). We left Florida for two years, including my year in Whittier (Dad was in South Korea for a year, we stayed in Whittier where we had our relatives) and Montgomery Alabama--another damn suburb pretty far from Maxwell AFB, much farther than I'd think of bicycling. When we returned to PC in 1976, we got another house, this one in that neighborhood with the swamp. Again our house abutted on what appeared to be raw wilderness, but this jungle was much thicker, no crossing the fence into this, it was all blackberry brambles in the underbrush--but there was a way around and there was this "bridge," actually a raised conduit for some sort of pipe, probably sewage, not at all meant for people to walk on. We kids did anyway, and it went over swamp, I remember seeing water moccasins in it. Actually I think a lot of this stuff was the sewage treatment.
So yeah, this kind of thing was shortcuts between separate (grid laid out) developments, and kids would make or find paths through it, but it was not intended by any planners for people to do that! On paper I suppose now we are all trespassing, and quite proximate to a bunch of hazards.
It was kind of like that in Montgomery where I lived a year, 5th grade, too. We had a slightly curved road semi-grid little "neighborhood" of houses, no park. One could however strike out across a big undeveloped tract, dunno if I could call it a "meadow" or not. Walking across this grass and mud, I eventually came to the road that led to the church and Catholic school me and my sisters went to; driving it involved a really long loop out of the way we had to ride on every day except Saturday. In another direction, roads led to denser developments that were close to continuous, no actual cul de sacs, the roads did wind a bit. Eventually one came to a big highway and there were various stores there, and at some further distance a mall. Elsewhere in Montgomery there were interesting things I saw rarely, even a planetarium. I got taken to the AFB a lot though, a long drive with my Dad usually. I was allowed to use the base library and started borrowing books from the adult section (science fiction exclusively, this is when I started to catch up on SF pretty closely--I still found some books of interest in the children's section, but mostly it was the adult SF books I came for). Also got to enter the Air University library, which was pretty impressive to me, it had double sets of doors like an airlock to preserve some of the older books and other documents. (The USAF sends its officers to Montgomery, Alabama for culture and enlightenment).
I guess I had more experience of interesting layouts on the Air Force bases than in the kinds of slurbs my Dad would buy houses in.
This tour guide pretty well covers my experience of residences in my K-12 years except for the couple years we lived on Langley AFB when I was in high school. Langley was actually cool as Air Force bases go being the most ancient (maybe not the single oldest, but one of the very oldest) bases, as an old Signal Corps base in fact, also of course the home of N.A.C.A.
So in all these mostly Southern, mostly just middling developed, places, I never saw either the classic cul de sac nor the proper rigorous grid system. It was semi-organic, semi developer fiefdom.
I did take a class in the history of Southern California towns at Pasadena City College once. (The teacher was about as bad as any I have had the misfortune to deal with in post-K-12 years). The takeaway was that Los Angeles as I knew it was the product of a bunch of real estate brokers getting ahold of some chunk or other and developing the heck out of it. In LA County there were definitely some parks, but the major definition of space was commercial. I never really witnessed integrated commercial/residential, there was always some serious separation of residence from any other function, typically a matter of highways having businesses of various kinds all along them, with the residential neighborhoods having major branch fast roads running through them without houses on them directly, you had to turn off these thoroughfares to come to the lawns and driveways. I guess some sort of zoning prevented businesses from existing on these highways.
As an adult I lived in Pasadena '83-91, and then we (I met someone) lived by mistake as it were in Humboldt County CA until she could finagle a way the heck out of there down to Sonoma County, where we were much happier. In Humboldt too, I don't recall a lot of classic cul de sac, more of this somewhat twisty grid system as in the South. In Santa Rosa, I think there were more of those cul de sacs than I'd seen before but mostly it was again twisty grid systems, there and in Sebastapol and Petaluma and Healdsburg. We ourselves lived a quarter mile up a gravel driveway in a rural shadow zone behind the county airport. Then my partner died, and I wound up moving out some years later to Nevada where I have seen lots of these classic cul de sacs.
I take my 3 year old niece to the park pretty often. I am here to tell you there is no nice shortcut way from this house on a cul de sac to the park; if I could tunnel through the house across the street we'd be right there, but no, we have to go to the other end of the road, go around and get to the park that way. There is a nice dog walk (for a certain spartan value of nice) that runs through two large blocks with no car access, but this is quite exceptional. Urban Washoe county is the place most devoted to classic US cul de sacs and twisty roads, I have no freaking clue where I am if I turn off the main highways that form a sort of meta-grid. Downtown Sparks is more griddish, and downtown Reno is a bunch of different grids all turned at different angles. The massive new developments are a jungle of tangled twisty roads and cul de sacs.
And no one
provides paths between the isolated Bag Ends. If they exist, they are outlaw. I understand that British law protects footpaths that have existed "From time immemorial" and people have rights to walk on private property. Not here! Many places might leave it de facto possible as in my childhood, due to lax oversight and enforcement, I presume someone owned all those "jungles" and "woods" in the outlying parts of Panama City I wandered in. But private property is pretty much king here and with any serious development there is no commons. Courts have ruled shopping centers are kind of sort of commons, and that's where political petition drives and so forth happen, there or in parks.